合成人造地震动的非线性解法

Generation of Artificial Earthquake Wave by Non-linear Solver

提出了一种合成具有高的收敛精度的人造地震动的简易方法 .首先 ,从单质点系在地震作用下的反应出发 ,直接推导了求解与目标反应谱拟合的人造地震动基本公式 ;随后 ,利用插值函数将积分方程变换为代数方程组 ,进而从反应谱的变分求得人造地震动的时域变分 .我们将证明上述代数方程组是一非线性方程组 ,因而方程组的求解和收敛准则可以使用非线性方程组的经典解法 .本文提出的方法的特点是 ,充分利用传统的生成人造地震动的理论、方法和计算机程序 ,因此简单易行 .实例计算表明 ,文中提出的拟合方法 ,具有较高的收敛精度和较少的计算时间 .

A simple method of high precision is presented,which is used to generate artificial earthquake wave compatible with object response spectra.First,the basic formulas solving the artificial earthquake wave compatible with object response spectra are established;the integration equations are translated into the algebraic equations by interpolation function.Second,the variation of artificial earthquake wave in time domain is acquired from the variation of object response spectrum.The above mentioned equation groups are proved to be non linear,which can be solved by classical method.We will full make of the traditional theory,method,and computer codes for artificial earthquake motion,which make the method presented in this paper simple and easy.The example shows the high precision of the method and a little additional computer time.